In the latest installment of Le Jour où tout a basculé, we find two very different uses of the verb passer. The first is a direct cognate of the English verb "to pass," referring to time passing:

Quatre mois ont passé.

Four months have passed.

Caption 30, Le Jour où tout a basculé - Mon père s'oppose à ma passion - Part 6

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The second, referring to taking an exam, is a false cognate. You might assume that passer son bac means "to pass one's baccalaureate exam." But that's wrong! Passer in this context actually means "to take":  

J'ai passé mon bac.

I took my baccalaureate.

Caption 41, Le Jour où tout a basculé - Mon père s'oppose à ma passion - Part 6

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If you want to talk about passing an exam, use the verb réussir (to succeed):

Demain il réussira son examen.

Tomorrow he will pass his exam.

Caption 27, Le saviez-vous? - Conjugaison des verbes du 2ème groupe au futur simple

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Passer's other meanings are more predictable. You can use it transitively (i.e., with an object) to to talk about passing something to someone:

Passe le micro.

Pass the mic.

Caption 54, Arles - Le marché d'Arles

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Or you can use it intransitively (without an object) to describe someone passing by or passing from one place to another:

Tous les ans, effectivement, nous demandons à Saint-Nicolas de passer.

Every year, in fact, we ask Saint Nicholas to pass by.

Caption 44, Grand Lille TV - Focus: la tradition de Saint-Nicolas

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Et maintenant on va passer en cuisine avec le chef.

And now we'll go into the kitchen with the chef.

Caption 33, Parigot - Le bistrot

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Just as you can "pass time" (or "spend time") in English, you can passer du temps in French: 

Et puis ça permet de passer un bon petit moment ensemble.

And then it allows us to spend a good bit of time together.

Caption 47, Actus Quartier - Fête de quartier Python-Duvernois - Part 2

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The expression passer pour means "to pass for," as in "to be taken for" or "seem like":

La maîtrise des synonymes vous permettra donc d'élargir votre vocabulaire, mais aussi, de ne pas passer pour un psychopathe.

Mastering synonyms will therefore allow you to broaden your vocabulary, but also to not be taken for a psychopath.

Captions 23-24, Le saviez-vous? - Les synonymes

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As passer is such a versatile verb, it's no surprise that it's used in many, many common expressions. We'll pass along a handful of them to you:

passer à autre chose - to move on to something else
passer à l'acte - to take action
passer à la caisse - to pay/checkout
passer à la télévision - to be on TV
passer à table - to sit down for a meal (also has the figurative meaning "to snitch" or "spill the beans")
passer un coup de fil - to make a phone call
passer de la musique - to put on some music
passer au bloc - to go under the knife/have surgery
passer au peigne fin - to go over with a fine-tooth comb
passer à côté de - to miss/miss out on
laisser passer sa chance - to miss one's chance

You can find even more expressions on this WordReference page.

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And to learn about the reflexive form of passer, se passer, check out our lesson Se Passer: To Bypass and Pass By.